Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 6, Problem 25P
To determine
Verify that the oscillator energies in equation 6.29 correspond to the classical amplitudes.
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Starting with the equation of motion of a three-dimensional isotropic harmonic
ocillator
dp.
= -kr,
dt
(i = 1,2,3),
deduce the conservation equation
dA
= 0,
dt
where
1
P.P, +kr,r,.
2m
(Note that we will use the notations r,, r2, r, and a, y, z interchangeably, and similarly
for the components of p.)
Consider the half oscillator" in which a particle of mass m is restricted to the region x > 0 by the potential energy
U(x) = 00
for a O
where k is the spring constant.
What are the energies of the ground state and fırst excited state? Explain your reasoning.
Give the energies in terms of the oscillator frequency wo =
Vk/m.
Formulas.pdf (Click here-->)
Q # 01: Consider a ball of 100g dropped with zero velocity from the height of 2m.
Estimate its total energy in eV units.
Using the energy conservation, find out the velocity as a function of position of the ball. Sketch its phase trajectory.
Calculate the time it takes to reach the ground.
Let’s assume that it is bounced back with no loss in its total energy.Will it reachthe same height? Make an analytical argument.
What if the collision with the ground is not elastic and it loses some of its energy (which energy?).The ball will eventually come to rest after bouncing few times. Sketch the phase trajectory for the whole duration.
What is the range of total energy of this system? Can the energy of this systemassume discrete values? Explain mathematically.
Chapter 6 Solutions
Modern Physics
Ch. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.5 - Prob. 4ECh. 6.7 - Prob. 5ECh. 6.8 - Prob. 6ECh. 6 - Prob. 1QCh. 6 - Prob. 2QCh. 6 - Prob. 3QCh. 6 - Prob. 4QCh. 6 - Prob. 5Q
Ch. 6 - Prob. 6QCh. 6 - Prob. 7QCh. 6 - Prob. 8QCh. 6 - Prob. 1PCh. 6 - Prob. 2PCh. 6 - Prob. 3PCh. 6 - Prob. 5PCh. 6 - Prob. 6PCh. 6 - Prob. 7PCh. 6 - Prob. 8PCh. 6 - Prob. 9PCh. 6 - Prob. 10PCh. 6 - Prob. 11PCh. 6 - Prob. 12PCh. 6 - Prob. 13PCh. 6 - Prob. 14PCh. 6 - Prob. 15PCh. 6 - Prob. 16PCh. 6 - Prob. 17PCh. 6 - Prob. 18PCh. 6 - Prob. 19PCh. 6 - Prob. 21PCh. 6 - Prob. 24PCh. 6 - Prob. 25PCh. 6 - Prob. 26PCh. 6 - Prob. 28PCh. 6 - Prob. 29PCh. 6 - Prob. 30PCh. 6 - Prob. 31PCh. 6 - Prob. 32PCh. 6 - Prob. 33PCh. 6 - Prob. 34PCh. 6 - Prob. 35PCh. 6 - Prob. 37PCh. 6 - Prob. 38P
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